Safety brakes are used in emergency situations when due to technical problems or misbehavior of persons the step belt of the escalator or the plate belt of the moving walkway has to be rapidly stopped. In one example of a safety brake, the locking member or pawl is mounted to be pivotable about a pivot axis. The locking member is held by an actuating element in a release setting. As soon as the actuating element is activated, this pivots the locking member about the pivot axis into a locking setting so that the locking member engages in a moved part of the escalator or the moving walkway and blocks this. The moved part in which the locking member engages is usually a wheel rotatable about an axis of rotation. This can be, for example, a deflecting wheel of the step belt or a transmission wheel of a drive train connecting a drive motor with the step belt to be driven.